Inspect members ui does not get focus when opened. It's opening in the front, but when you start typing everything goes to last focused editor.
I think best would be that "Filter:" field gets focus when opening members UI.

I tried this on 7.1, 7.1.1, and on the daily build with JDK 1.6u29. In all cases it works as expected, i.e, the focus is in Filter: field upon Inspect Members dialog opening. What JDK version do you use ? Can you observe the faulty behavior also on other machines ?